The flare is the part of the landing where the nose is lifted up slightly instead of being level (descending) in order to:
a) arrest the descent
b) make sure the main wheels come into contact with the tarmac first and not the nose-wheels
c) make sure the airplane wing 'stalls' at exactly the right time so that the aircraft makes contact with the pavement.

As for where Rotate comes from (yes we all know what it is) maybe it comes from the aircraft rotating around its main undercarriage, instead of using, say, Pull Up, which, while the action is the same (pulling the yoke back) incurs that you are already flying and need to get higher.